You may be able to find your ship in the server-database folder within the StarMade folder, but I'm not sure if that would work to copy-paste, I'm doubtful of that. It may be simpler to get your Starmade working. You could get a fresh installation of StarMade, but backup your server-database folder, and your blueprints folder (if you have any blueprints you want saved). Then re-install StarMade, replace those folders in the new StarMade folder with the server-database folder and/or blueprints folder you saved, and then try running the game. This will ensure that the base game files are as they should be, and your world with all your ships will remain just as before.
If you still cannot get StarMade to run, then it would be helpful to know if you get any errors and if so, what are they? Does your game load to 100% then crash? Or is something else not right? Perhaps there is a problem with your Java or you are experiencing a bug due to your computer hardware? Without knowing those things, it is difficult to understand and fix the problem if StarMade is not working.